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A bookstore has a shelf that contains biographies which
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Updated on: 22 Oct 2012, 08:56
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72% (03:03) correct 28% (03:15) wrong based on 58 sessions
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A bookstore has a shelf that contains biographies which normally sell for $20 each and mysteries that normally sell for $12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 35 percent, wha is the discount rate on mysteries? (A) 9 (B) 10 (C) 13 (D) 22 (E) 25
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Originally posted by Anichka on 22 Oct 2012, 03:46.
Last edited by Bunuel on 22 Oct 2012, 08:56, edited 1 time in total.
Renamed the topic.



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Re: Discounted books in a store
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22 Oct 2012, 04:45
Anichka wrote: A bookstore has a shelf that contains biographies which normally sell for $20 each and mysteries that normally sell for $12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 35 percent, wha is the discount rate on mysteries?
(A) 9 (B) 10 (C) 13 (D) 22 (E) 25 Let B be the discount on biographies and M be the discount on mysteries So., B + M = 0.35 (1) And (20*5 + 12*3)  (20*5*(1B) + 12*3*(1M)) = 19 > 100(1(1B)) + 36(1(1M) = 19 100B + 36M = 19 (2) Solving 1 & 2., we get M = 0.25 = 25%
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Re: Discounted books in a store
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22 Oct 2012, 06:03
Thanks! It works out now.
I have though a question. In the problem it says: "The biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries."
Doesn't that mean that when 5 biographies and 3 mysteries are purchased, the total amount will be 19 less than if the books have not been discounted, meaning, 5*20 + 3*12 = 136 (this would be if they kept the original price). But after the discount ( (5*20  5*20*b%) + (3*12  3*12*m%) = 136  19. Then, the equation doesn't work.
Thank you for your reply!



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Re: Discounted books in a store
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22 Oct 2012, 07:45
Anichka wrote: Thanks! It works out now.
I have though a question. In the problem it says: "The biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries."
Doesn't that mean that when 5 biographies and 3 mysteries are purchased, the total amount will be 19 less than if the books have not been discounted, meaning, 5*20 + 3*12 = 136 (this would be if they kept the original price). But after the discount ( (5*20  5*20*b%) + (3*12  3*12*m%) = 136  19. Then, the equation doesn't work.
Thank you for your reply! You should note that it should be 5*20*(1b) and 3*12*(1m). To make it more clear. Suppose an item costs $100. And now I am going to give a discount of 20%. The new price would not be $20 (i.e 100*0.2) rather it would be $80 (i.e 100*(10.2)). When you are discounting a price P by x%, the discounted price will be \(P*(1  \frac{x}{100})\) and not \(\frac{P*x}{100}\) Kudos Please... If my post helped.
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Re: Discounted books in a store
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22 Oct 2012, 08:02
Anichka wrote: A bookstore has a shelf that contains biographies which normally sell for $20 each and mysteries that normally sell for $12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 35 percent, wha is the discount rate on mysteries?
(A) 9 (B) 10 (C) 13 (D) 22 (E) 25 Another way to translate into equations: M  percent discount on one mystery book B  percent discount on one biography book B + M = 35 5x20xB/100 + 3x12xM/100 = 19  the saving of $19 comes from the discounts, which can be directly expressed in terms of M and B, respectively, for the two types of books. Solve the system of two equations: B + M = 35 100B + 36M = 1900 Or: From the answers, we can see that M should be an integer. Because 100 and 1900 are both divisible by 5, only B and E should be checked. Answer E.
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Re: Discounted books in a store
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22 Oct 2012, 08:12
i didnt understand what is (1b) and (1m) pls explain in detail



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Re: Discounted books in a store
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22 Oct 2012, 08:46
Archit143 wrote: i didnt understand what is (1b) and (1m) pls explain in detail An item costs $100. I am now going to give a discount of b% on it. So my new price would be \(100  100*(\frac{b}{100})\) \(=\) \(100*(1\frac{b}{100})\) If we take b% in the decimal form. ( eg: 20% as 0.2) then the above equation would be \(100*(1b)\) Kudos Please... If my post helped.
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A bookstore has a shelf that contains biographies which
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20 Nov 2015, 01:57
I got the right answer but only after 5 mins. The difficulty is the precision in calculations. How to reduce time on these questions yet still maintain precision?! Thanks very much in advance.



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Re: A bookstore has a shelf that contains biographies which
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13 Mar 2018, 17:05
Anichka wrote: A bookstore has a shelf that contains biographies which normally sell for $20 each and mysteries that normally sell for $12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 35 percent, wha is the discount rate on mysteries?
(A) 9 (B) 10 (C) 13 (D) 22 (E) 25 We can let x = the percent by which the biographies are discounted, and thus, (35  x) = the percent by which the mysteries are discounted. Just as we can express, say, 42% as 42/100, we will express x% as x/100, and, similarly, (35  x)% is reexpressed as (35  x)/100. We can create the following equation: 5 * 20 * x/100 + 3 * 12 * (35  x)/100 = 19 Multiplying both sides by 100, we have: 100x + 36(35  x) = 1900 100x + 1260  36x = 1900 64x = 640 x = 10 Thus, the mysteries are discounted by 35  10 = 25 percent. Answer: E
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Re: A bookstore has a shelf that contains biographies which &nbs
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